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My boss asked a simple question today but I couldn't find the right answer.

He asked: If I had \$5,000 today in cash, the inflation is 2% year-over-year, then then what's its buying power (value) after 50 years?

If I use the following formula: $5000 * (1-0.02)^{50}$ I get \$1820.

However if I use inflation calculator (at this website http://www.buyupside.com/calculators/inflationjan08.htm) that uses present value/future value formula, I get a different result: $\frac{5000}{(1+0.02)^{50}}$ I get \$1,857.

Which formula is correct and why?

Josh
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  • The inflation rate has been given, not the depreciation rate of the buying power of money, so the second formula is correct. – true blue anil Jul 03 '16 at 06:12
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    I don't understand the difference. Inflation rate is depreciation rate in this case. Today I had $5,000 and after 1 year inflation ate 2% of it, so while I still have $5,000 in my pocket, my money is worth only $4,900. Extending this for 50 years, I get that the first formula is correct. Can you please explain in more details. Please use simple terms. I don't know the difference between inflation, depreciation, buying power and future/present value. I only learned about these terms today. I studied math 25 years ago. I still remember some basic formulas, such as first one but not much more. – Josh Jul 03 '16 at 06:16
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    Suppose you are buying wheat,say. Inflation rate of $2%$ means that an amount of wheat that costs $$100$ today will cost $$102$ next year. Depreciation in the buying power of money means that your $$100$ today can buy only $$98$ worth of wheat next year. $100*1.02 = 102, 100/0.98 = 102.04... The two aren't the same. – true blue anil Jul 03 '16 at 06:26
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    Inflation doe s not "eat" $2%$ of your money, it makes goods $2%$ costlier. With your $$5000$, next year your money would be worth $5000/1.02 = 4901.96. – true blue anil Jul 03 '16 at 06:32
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    You can understand the difference clearly as you hike up the inflation rate. A $100%$ inflation rate doesn't mean that your money can't buy anything next year with it ! You can buy half of what you could buy this year ! – true blue anil Jul 03 '16 at 06:40

2 Answers2

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In Zimbabwe, they had a 79,600,000,000% inflation rate. So if you had $ 5000$ dollars, according to your formula you would have $5000(1-796,000,000)=-3979999995000$ dollars. Does this sound right?

However the second formula gives $\frac{5000}{1+796,000,000}=6.2814070272846645385871048510212\times 10^{-6}$.

What one sounds more reasonable?

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HINT

Inflation is a sustained increase in the general price level of goods and services in an economy over a period of time.

The inflation rate $i_{t}$ between year $t - 1$ and year $t$ is calculated as $$ i_t=\frac{\text{change in price}}{\text{price in year }t - 1} = \frac {P_{t}-P_{t-1}}{P_{t-1}} =\frac {P_{t}}{P_{t-1}}-1 $$ that is $$P_t=P_{t-1}(1+i_t)$$ or $$ P_{t-1}=\frac{P_t}{1+i_t} $$

alexjo
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